The Second Law of Thermodynamics

Study Notes: Introduction to the Second Law of Thermodynamics

• While the first law of thermodynamics focuses on the conservation of energy, it doesn't address the direction in which processes occur. [1]

• The second law of thermodynamics complements the first law by:

• Establishing the direction of processes, indicating that they proceed in a specific direction, not spontaneously in reverse. [2]

• Recognising that energy possesses quality in addition to quantity. [3]

• A process must adhere to both the first and second laws of thermodynamics to occur. [2]

Key Concepts

• Thermal Energy Reservoirs: Hypothetical bodies with large thermal energy capacity that can exchange heat without changing temperature. Examples include oceans, lakes, and the atmosphere. [4, 5]

• Heat Engines: Devices that operate in a cycle, receiving heat from a high-temperature source, converting some to work, and rejecting waste heat to a low-temperature sink. [6]

• Thermal Efficiency: The ratio of net work output to total heat input, measuring a heat engine's effectiveness. [7]

• Refrigerators: Cyclic devices that transfer heat from a low-temperature space to a high-temperature environment, requiring work input. [8, 9]

• Coefficient of Performance (COPR): Indicates a refrigerator's efficiency, defined as the ratio of heat removed from the cooled space to the required work input. [10]

• Heat Pumps: Similar to refrigerators, heat pumps transfer heat from a low-temperature source to a high-temperature space, but their objective is heating. [11]

• Coefficient of Performance (COPHP): Measures a heat pump's efficiency, defined as the ratio of heat supplied to the heated space to the required work input. [12]

Statements of the Second Law

• Kelvin-Planck Statement: It's impossible for a cyclic device to receive heat from a single reservoir and produce net work. In other words, a heat engine must reject some heat to a low-temperature sink for continuous operation. [13]

• Clausius Statement: It's impossible to construct a device that operates in a cycle, producing no effect other than transferring heat from a lower-temperature body to a higher-temperature body. In other words, external work input is needed to transfer heat from cold to hot. [14]

• Both the Kelvin-Planck and Clausius statements are negative and equivalent expressions of the second law. [15]

Perpetual-Motion Machines

• Perpetual-motion machines are hypothetical devices that violate either the first or second law of thermodynamics. [16]

• Perpetual-motion machine of the first kind (PMM1): Violates the first law by creating energy. [16]

• Perpetual-motion machine of the second kind (PMM2): Violates the second law. For example, a heat engine claiming 100% efficiency. [16, 17]

Reversible and Irreversible Processes

• Reversible processes are idealised processes that can be reversed without leaving any trace on the surroundings. [18]

• They are theoretical limits for corresponding irreversible processes, which occur in reality. [19]

• Irreversibilities are factors that cause a process to be irreversible. Examples include: [20]

• Friction [21]

• Unrestrained expansion [21]

• Heat transfer across a finite temperature difference [22]

• Mixing of fluids [20]

• Electric resistance [20]

• Inelastic deformation [20]

• Chemical reactions [20]

• Minimising irreversibilities in engineering systems maximises efficiency. [19]

Internally and Externally Reversible Processes

• A process is internally reversible if no irreversibilities occur within the system boundaries. [23]

• A process is externally reversible if no irreversibilities occur outside the system boundaries. [23]

• A process is totally reversible (simply reversible) if it involves no irreversibilities within the system or its surroundings. [24]

Carnot Cycle

• The Carnot cycle is a theoretical cycle consisting of four reversible processes: [25-27]

1. Reversible Isothermal Expansion

2. Reversible Adiabatic Expansion

3. Reversible Isothermal Compression

4. Reversible Adiabatic Compression

• The Carnot cycle is the most efficient cycle operating between two specific temperature limits. [28]

• Reversed Carnot Cycle: The Carnot cycle can be reversed to represent a refrigeration cycle, where the direction of heat and work interactions are flipped. [28]

Carnot Principles

1. Efficiency Comparison: The efficiency of an irreversible heat engine is always less than the efficiency of a reversible heat engine operating between the same two reservoirs. [29, 30]

2. Efficiency Equality: The efficiencies of all reversible heat engines operating between the same two reservoirs are the same. [29, 31]

Thermodynamic Temperature Scale

• A thermodynamic temperature scale is independent of the properties of substances used to measure temperature. [32]

• The Kelvin scale is a thermodynamic temperature scale where the ratio of absolute temperatures is defined based on the ratio of heat transfers between a reversible heat engine and the reservoirs. [33]

• Absolute Zero: The theoretical lower limit of temperature, 0 K or -273.15°C, where molecular motion ceases. [33]

• Triple Point of Water: The state where all three phases of water exist in equilibrium, assigned the value of 273.16 K. [34]

Carnot Heat Engine

• The Carnot heat engine is a hypothetical engine operating on the reversible Carnot cycle. [35]

• Its efficiency is the maximum possible for any heat engine operating between the same temperature limits: [35]

• ηth,rev = 1 - TL/TH

• where TL and TH are the absolute temperatures of the low- and high-temperature reservoirs, respectively.

• The efficiency of a Carnot heat engine increases with increasing TH and decreases with increasing TL. [36]

Carnot Refrigerator and Heat Pump

• Carnot refrigerator and Carnot heat pump are hypothetical devices operating on the reversed Carnot cycle. [37]

• Their COPs are the maximum possible for any refrigerator or heat pump operating between the same temperature limits: [37]

• COPR,rev = TL / (TH - TL)

• COPHP,rev = TH / (TH - TL)

• The COPs of actual refrigerators and heat pumps are always lower than the corresponding Carnot COPs. [38]

The Quality of Energy

• Higher-temperature thermal energy can be converted to work more efficiently, indicating a higher quality of energy. [39]

• The sources only mention the quality of energy in relation to its temperature. Information regarding other factors affecting energy quality would need to be independently verified.